Permutation or binomial expansion?

A group of 3 undergraduates and 5 graduate students are available to fill a position. If 4 students are to be randomly selected from this group find the probability that exactly 2 undergraduates will be among the chosen 4.

I'm thinking that I have to resolve this problem using a binomial expansion with which gives me possible ways of filling the post and then to find the number of undergrads and for the number of grads. which would give me a final solution of

A group of 3 undergraduates and 5 graduate students are available to fill a position. If 4 students are to be randomly selected from this group find the probability that exactly 2 undergraduates will be among the chosen 4.

I'm thinking that I have to resolve this problem using a binomial expansion with which gives me possible ways of filling the post and then to find the number of undergrads and for the number of grads. which would give me a final solution of